hdu-5391-Zball in Tina Town

题目链接：http://acm.split.hdu.edu.cn/showproblem.php?pid=5391

Zball in Tina Town

Problem Description

Tina Town is a friendly place. People there care about each other.

Tina has a ball called zball. Zball is magic. It grows larger every day. On the first day, it becomes  1 time as large as its original size. On the second day,it will become  2times as large as the size on the first day. On the n-th day,it will become  n times as large as the size on the (n-1)-th day. Tina want to know its size on the (n-1)-th day modulo n.

 

Input

The first line of input contains an integer  T, representing the number of cases.

The following  T lines, each line contains an integer  n, according to the description.
T≤105,2≤n≤109

 

Output

For each test case, output an integer representing the answer.

 

Sample Input

2 3 10

 

Sample Output

2 0

 

题目分析：一个球初始体积为1，一天天变大，第一天变大1倍，第二天变大2倍，第n天变大n倍。问当第 n-1天的时候，体积变为多少。注意答案对n取模。也就是说第一天是1，第二天是1*2，第三天是1*2*3，也就是当第n天的时候是n!。那么答案就是（n-1）! % n。
题目里面n是10^9，直接阶乘肯定不行，找规律发现，如果是素数，答案就是n-1，否则就是0。4是个例外，n=4时输出2，于是问题就转化成为求n是否为素数！！！

#include 
#include 
#include 
#include 
using namespace std;
int prime(int n)
{
	for(int i=2; i*i<=n; i++)
		if(n % i == 0)
			return 0;
	return 1;
}
int main()
{
	int T;
	scanf("%d",&T);
	while(T--)
	{
		int n;
		scanf("%d",&n);
		if(n == 4) printf("2\n");
		else if(!prime(n)) printf("0\n");
		else printf("%d\n",n-1);
	}
}